PASE: A Massively Parallel Augmented Subspace Eigensolver for Large Scale Eigenvalue Problems

TL;DR

This paper introduces PASE, a parallel augmented subspace eigensolver that efficiently solves large-scale eigenvalue problems by transforming them into linear equations and low-dimensional eigenproblems, demonstrating high scalability and efficiency.

Contribution

The paper presents a novel massively parallel augmented subspace method and a corresponding software package, improving scalability and efficiency for large eigenvalue problems.

Findings

Demonstrates high scalability of PASE on large problems

Shows efficiency comparable to solving linear equations of similar size

Validates method with numerical examples

Abstract

In this paper, we present a novel parallel augmented subspace method and build a package Parallel Augmented Subspace Eigensolver (PASE) for solving large scale eigenvalue problems by the massively parallel finite element discretization. Based on the augmented subspace, solving high dimensional eigenvalue problems can be transformed to solving the corresponding linear equations and low dimensional eigenvalue problems on the augmented subspace. Thus the complexity of solving the eigenvalue problems by augmented subspace method will be comparable to that of solving the same dimensinal linear equations. In order to improve the scalability and efficiency, we also present some implementing techniques for the parallel augmented subspace method. Based on parallel augmented subspace method and the concerned implementing techniques, a package PASE is built for solving large scale eigenvalue problems. Some numerical examples are provided to validate the efficiency and scalability of the proposed numerical methods.